If f(x)= x^ n -a^ n x-a for some constant, a, then f'(a) is equal… - Vidyadip

MCQ

If $\text{f}(\text{x})=\frac{\text{x}^{\text{n}}-\text{a}^{\text{n}}}{\text{x}-\text{a}}$ for some constant, $a,$ then $f'(a)$ is equal to:

A
$1$
B
$0$
✓
Does not exist
D
$\frac{1}{2}$

✓

Answer

Correct option: C.

Does not exist

Given $\text{f}(\text{x})=\frac{\text{x}^{\text{n}}-\text{a}^{\text{n}}}{\text{x}-\text{a}}$
$\text{f'}(\text{x})=\frac{(\text{x}-\text{a})(\text{n.}\text{x}^{\text{n-1}}-(\text{x}^{\text{n}-\text{a}^{\text{n}}})1}{(\text{x}-\text{a})^{2}}$
So, $\text{f}(\text{a})=\frac{0}{0} =$ Does not exist.

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